Whether the US claim is truthful or not doesn't matter. China's mistake was to even give the US the chance to credibly make such a claim. If (as I recommended a year ago) China had invaded Manchuria immediately after Russia invaded Ukraine, no one would take seriously any subsequent US claim that China was supplying Russia, and thus the US would refrain from such a claim in the first place.
As I keep saying, the only way to gain the trust of one side is to voluntarily burn bridges to the other side:
https://trueleft.createaforum.com/issues/china-and-united-states-relations/msg11788/?topicseen#msg11788